** Authors:**
SAYED KHALIL EKRAMI, MADJID MIRZAVAZIRI

** Abstract: **
Let $\mathcal{A}$ be an algebra. A linear mapping $d:\mathcal{A}\to\mathcal{A}$ is called a *derivation* if $d(ab)=d(a)b+ad(b)$ for each $a,b\in\mathcal{A}$. Given two derivations $d$ and $d'$ on a C$^*$-algebra $\mathcal{A}$, we prove that there exists a derivation $D$ on $\mathcal A$ such that $dd'+d'd=D^2$ if and only if $d$ and $ d' $ are linearly dependent.

** Keywords: **
Derivation; C$^*$-algebra

** Full Text:** PDF